Two- and three-dimensional transient melt-flow simulation in vapour-pressure-controlled Czochralski crystal growth

Journal article
(Original article)


Publication Details

Author(s): Bänsch E, Davis D, Langmach H, Reinhardt G, Uhle ME
Journal: Computers & Fluids
Publisher: Elsevier
Publication year: 2006
Volume: 35
Journal issue: 10
Pages range: 1400-1419
ISSN: 0045-7930


Abstract


Flow and thermal properties associated with semiconductor melt flow in an axisymmetric crucible container are studied numerically. Axisymmetric and three-dimensional computational solutions are obtained using a standard-Galerkin, finite-element solver. The crucible and crystal are optionally rotated, and the influence of gravity (through buoyancy) is accounted for via a Boussinesq approximation in the controlling Navier–Stokes equations. The results indicate a strong dependence of the flow on both rotation and buoyancy. Results for axisymmetric flows, computed with both flat and curved geometries, are presented first, and strongly suggest that rotation of crystal and crucible in the same direction (iso-rotation) is most favourable for producing a desired convexity for the crystal/melt interface. Three-dimensional results are then presented for higher Reynolds numbers, and, in particular, reveal that for iso-rotation under moderate buoyancy, the flow undergoes a switch from a steady 2D state to an unsteady 3D state, and that the temperature becomes non-trivially advected by the flow beneath the crystal. Further evidence reveals however, that on a time scale more appropriate to the crystal growth process, the (time-averaged) flow has a weaker three-dimensionality, in relation to the mean axisymmetric part, and there is only slight distortion to the temperature field beneath the crystal. A detailed examination of the instability properties is also made, revealing the underlying nonlinear mode interaction and associated frequency responses around the bifurcation point.



FAU Authors / FAU Editors

Bänsch, Eberhard Prof. Dr.
Lehrstuhl für Angewandte Mathematik (Wissenschaftliches Rechnen)


How to cite

APA:
Bänsch, E., Davis, D., Langmach, H., Reinhardt, G., & Uhle, M.E. (2006). Two- and three-dimensional transient melt-flow simulation in vapour-pressure-controlled Czochralski crystal growth. Computers & Fluids, 35(10), 1400-1419. https://dx.doi.org/10.1016/j.compfluid.2005.01.004

MLA:
Bänsch, Eberhard, et al. "Two- and three-dimensional transient melt-flow simulation in vapour-pressure-controlled Czochralski crystal growth." Computers & Fluids 35.10 (2006): 1400-1419.

BibTeX: 

Last updated on 2018-23-07 at 02:10